= Solution
Let $\widehat\theta_n$ be the MLE and let $I(\theta)$ be the one-observation Fisher information <matrix>. One standard form of the Wald statistic is
$$
\boxed{W_n(\theta)
=n(\widehat\theta_n-\theta)^T
I(\widehat\theta_n)(\widehat\theta_n-\theta)}.
$$
Any consistent information estimator gives the same asymptotics. Under $H_0$,
$W_n(\theta_0)\Rightarrow\chi_p^2$. If
$c_{p,\alpha}$ is the $(1-\alpha)$ quantile of $\chi_p^2$, reject when
$$
W_n(\theta_0)>c_{p,\alpha}.
$$
The asymptotic type-I error is $\alpha$.
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